1998 AMC 8 Problem 21
Attempt Problem 21 of the 1998 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1998 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
21.
A cubical box contains identical small cubes that exactly fill the box. How many of these small cubes touch a side or the bottom of the box?
Answer: B
Small hint:
Count the cubes that do not touch a side or the bottom.
Big hint:
The untouched interior core is
Solution:
The only cubes that do not touch a side or the bottom form the interior core above the bottom layer. This core has dimensions so it contains cubes.
Thus, cubes touch a side or the bottom.
Thus, the correct answer is B .
Problem 21 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
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- 1999 AMC 8
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